Suppose you have a standard deck 52 cards (4 suits: hearts, diamonds, clubs, and spades each suit has 13 cards (1/4 of the deck) and those 13 cards include one ace,and numbers 2 through 10 and 3 face cards: a jack a queen and king) suppose you pick a card at randome and then without replacement the first card you pick another card randomly.
1.) what is the probability that your second card is heart in general regardless of the card you drew first?
The probability that your second card is a heart is 1/4, or 25%.
To find the probability that your second card is a heart, regardless of the first card you drew, we need to consider the remaining cards in the deck after drawing the first card.
In the deck, there are initially 13 hearts out of 52 cards. After drawing the first card, there are 51 cards remaining in the deck, but the number of hearts remains the same (13).
Therefore, the probability of drawing a heart as the second card is:
P(Heart as second card) = Number of hearts / Total number of remaining cards
= 13 / 51
≈ 0.255 or 25.5%
To find the probability of picking a heart as the second card regardless of the first card you picked, we need to understand a few concepts.
First, let's determine the total number of cards in the deck when you pick the second card. Since you picked one card already, there are now 51 cards left in the deck.
Next, we need to determine the number of hearts in the remaining cards. Since the first card you picked does not affect the number of hearts in the deck, there are still 13 hearts remaining.
Therefore, the probability of picking a heart as the second card can be calculated as the ratio of the number of hearts remaining to the total remaining cards:
Probability = (Number of hearts remaining) / (Total remaining cards)
Probability = 13 / 51
Simplifying this fraction, we get:
Probability = 1/4
So, the probability of picking a heart as the second card, regardless of the first card you picked, is 1/4.